Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Obtuse scalene triangle.

Sides: a = 150   b = 200   c = 78.22204752788

Area: T = 5130.302214989
Perimeter: p = 428.2220475279
Semiperimeter: s = 214.1110237639

Angle ∠ A = α = 40.98661927479° = 40°59'10″ = 0.71553440113 rad
Angle ∠ B = β = 119.0143807252° = 119°50″ = 2.07771827919 rad
Angle ∠ C = γ = 20° = 0.34990658504 rad

Height: ha = 68.40440286651
Height: hb = 51.30330214989
Height: hc = 131.1755427702

Median: ma = 132.0398711658
Median: mb = 65.64546599231
Median: mc = 172.396602464

Inradius: r = 23.96110315062
Circumradius: R = 114.3510684902

Vertex coordinates: A[78.22204752788; 0] B[0; 0] C[-72.75330560674; 131.1755427702]
Centroid: CG[1.82224730705; 43.72551425674]
Coordinates of the circumscribed circle: U[39.11102376394; 107.4544494784]
Coordinates of the inscribed circle: I[14.11102376394; 23.96110315062]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.0143807252° = 139°50″ = 0.71553440113 rad
∠ B' = β' = 60.98661927479° = 60°59'10″ = 2.07771827919 rad
∠ C' = γ' = 160° = 0.34990658504 rad

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How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 150 ; ; b = 200 ; ; gamma = 20° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 150**2+200**2 - 2 * 150 * 200 * cos(20° ) } ; ; c = 78.22 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 150 ; ; b = 200 ; ; c = 78.22 ; ;

2. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 150+200+78.22 = 428.22 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 428.22 }{ 2 } = 214.11 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 214.11 * (214.11-150)(214.11-200)(214.11-78.22) } ; ; T = sqrt{ 26320000.15 } = 5130.3 ; ;

5. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5130.3 }{ 150 } = 68.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5130.3 }{ 200 } = 51.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5130.3 }{ 78.22 } = 131.18 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 150**2-200**2-78.22**2 }{ 2 * 200 * 78.22 } ) = 40° 59'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 200**2-150**2-78.22**2 }{ 2 * 150 * 78.22 } ) = 119° 50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 78.22**2-150**2-200**2 }{ 2 * 200 * 150 } ) = 20° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5130.3 }{ 214.11 } = 23.96 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 150 }{ 2 * sin 40° 59'10" } = 114.35 ; ;




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